The Romney and Obama campaigns — both convinced that their man is more trustworthy with the future of Medicare — ramped up the debate this weekend, with operatives trading prickly barbs, the president dismissing Republican plans as “snake oil” and Paul Ryan bringing his 78-year-old mother into the fracas.

“This is the first election cycle I can remember for a long time that Democrats are on the defensive with Medicare,” Romney senior adviser Eric Fehrnstrom said Sunday on CNN’s “State of the Union.”

Hoping to turn what has long been a political strength for Democrats into a liability, presumptive presidential nominee Mitt Romney and other Republicans are trying to hammer home charges that Mr. Obama “raided” Medicare by $700 billion in order to pay for other parts of his health care overhaul.

Mr. Romney launched the strategy last week, and Mr. Ryan, joined by his mother, Betty Ryan Douglas, continued the line of attack at an appearance Saturday before a crowd of thousands of mostly senior citizens at the Villages, a sprawling retirement community near Orlando, Fla.

“When I think of Medicare, it’s not just a program, it’s not just a bunch of numbers, it’s what my mom relies on,” he said. “We want this debate. We need this debate, and we’re going to win this debate.”

The Obama campaign pushed back aggressively. During his swing through New Hampshire on Saturday, the president called the Romney-Ryan economic plan “trickle-down snake oil.”

“Congressman Ryan he put forward a plan that would allow Gov. Romney to pay less than 1 percent in taxes each year,” the president said. “Their ideas are pretty simple — they’re not hard to explain. They think if we do more tax cuts for the very wealthiest Americans, then somehow prosperity’s going to rain down on all of us.”

Team Obama also dispatched deputy campaign manager Stephanie Cutter to the Sunday talk-show circuit, where she defended the Medicare savings created by the Affordable Care Act by insisting that most of the cuts came from trimming wasteful overpayments to private insurers.

The Medicare program is always a sticky wicket for politicians, but it has become front and center in the presidential contest ever since Mr. Romney chose Mr. Ryan as his running mate.

“Medicare should not be used as a piggy bank for Obamacare,” Mr. Ryan said Saturday.

A congressman from Wisconsin, Mr. Ryan is known for putting together a budget that would cut Medicare and turn it into a premium support system that allows seniors to use vouchers to buy private insurance.

But now that he is paired up with Mr. Romney, the two are promising to return all of Mr. Obama’s Medicare cuts if elected. While light on the details, they say their plan would offer premium vouchers beginning in 2023 while preserving the option of traditional Medicare.

The Republicans emphasize that their plan wouldn’t go into effect until 2023 and would have no effect on benefits for Americans 55 and older.

“Our solution to preserve, protect and save Medicare does not affect your benefits,” Mr. Ryan said. “Let me repeat that. Our plan does not affect the benefits for people who are in or near retirement.”

The Obama campaign says the Affordable Care Act’s reductions to future Medicare spending are derived largely from cutting overpayments to private insurers who participate in the alternative Medicare Advantage program.

The Congressional Budget Office has said Mr. Obama’s cuts extend the life of the Medicare trust funds by eight years, giving the government until 2024 to figure out a long-term solution to the troubled program.

“Here is the bottom line: My plan saves money in Medicare by cracking down on fraud and waste and insurance company subsidies, and their plan makes seniors pay more so they can give another tax cut to millionaires and billionaires,” Mr. Obama told voters in New Hampshire.

“My plan has already extended the life of Medicare by nearly a decade. Their plan would put Medicare on track to be ended as we know it,” he said.

Mr. Obama was referring to Medicare vouchers, which Republicans have proposed as an alternative to traditional Medicare but which Democrats say could leave seniors paying larger portions of their health care costs.

The president said Republicans were trying to distract from their own plan by attacking his health care law.

“The truth is, I think they know it’s not a very popular idea. You can tell that because now they’re being dishonest about my plans, since they can’t sell their plans,” he said, prompting laughter from the audience. “I mean, they are trying to throw everything at the wall just to see what will stick.”

With Florida perhaps the most important swing state in the November election, both campaigns are working overtime to sell their respective visions for the program. Medicare presents an easy opportunity to prey on emotions, as the cost of health care remains a top concern among voters.

In a reversal of roles, Republicans are arguing against cutting federal spending after trying to block increased federal spending for the past few years.

“There are people out there right now, many of whom are probably watching this program, who are probably shopping for new private health care because their Medicare Advantage program is being cut by this president,” Mr. Fehrnstrom said.

Democrats also are taking the opposite tack, focusing on approaching Medicare insolvency — a tune often sung by Republicans.

“If they put that savings back into the system, it means Medicare will go bankrupt in just four years,” Ms. Cutter said.